The former England centre-back was given the job on a caretaker basis following the decision to fire Sam Allardyce.
The former England centre-back was given the job on a caretaker basis following the Football Association's dramatic decision to dispense with Sam Allardyce, whose one-game reign was ended by controversial comments he made to undercover reporters.
Southgate has been in charge for England's past three games, including England's 3-0 win over old rivals Scotland in a World Cup qualifier at Wembley on Friday, a laboured victory over Malta and a goalless draw away to Slovenia.
His caretaker stint ends with Tuesday's friendly against Spain at Wembley and the 46-year-old, who has stepped up from the England Under-21 side, is clearly keen to stay on in the top job.
After the Spain clash England are not in action again until March and Southgate said: "It will be important for me to know what I'm doing after the middle of November.
"We've got a European Under-21 Championship to prepare for and the seniors have got their next round of qualifiers (in March).
"Of course everybody is going to want to know, I guess, by the end of November, middle of December, where everything is heading so we can decide who is responsible for which parts of the organisation's work.
"That's not my decision in the end. I've enjoyed what I've done so far.
"I'm immensely proud to have led my country for three games, with another on Tuesday, and to be involved in an England-Scotland game, which is as high-pressure as they come.
"It's been a brilliant experience and very, very special."
With England taking seven World Cup qualifying points from a possible nine and on course for Russia 2018, former Middlesbrough manager Southgate has gone some way to allaying fears about his lack of elite-level experience.
"I think if you look at a lot of the top coaches in the world they've had the opportunity at some point before they've worked at a big club," he said.
"Maybe you prove yourself at a smaller one first or maybe you don't. Pep (Guardiola) was straight in at Barcelona having worked with the B team.
"Everybody's path is different. I don't think there is an ideal pathway."
England captain Wayne Rooney, who returned to the starting line-up against Scotland, and defender Ryan Bertrand, an unused substitute on Friday, missed Monday's training session at Tottenham Hotspur's training ground in north London with what the Football Association said were "minor issues".